Is it okay to use "where" instead of "that" here?
Good question. In many cases, "that" and "where" are interchangeable in a sentence. In this case, you could replace "that" with "where" here, however, it would sound less natural to use "where" in this context. This is because she is not referring to a physical location when she says "place", but she is instead referring to a situation. So "that" here means "in which" while "where" often describes a physical location. Ex: This is the store where I bought my bike. Ex: This is the picture that I took.